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Distribution of IQ Scores

IQ scores have u = 100 and o = 15. The distribution is normal. A new drug is touted as having the effect of raising IQ by 10 points and we recruit a sample of n = 36 people to test it on. Using a=.05, how much power will we have? Please show work.

What is the probability of randomly selecting a red haired person from this distribution below?

Grey Brown Blonde Black Red
Eyes Blue 2 14 6 11 9
Green 4 17 8 9 8
Brown 6 19 9 28 9

Using the above chart what is the probability of selecting a blue eyed blond from this distribution?

Given that the probability that Nancy will wear blue to class is 20% and the probability that Tim will wear blue to class is 30%. What is the probability that they will both wear blue to class on same day?

What is probability that one of them will wear blue to class?

I am having difficulty with my formula's. I am taking an online class and cannot get it right. Just need some guidance.

Solution Preview

1.

Power is the probability of rejecting the null hypothesis given that the alternative hypothesis is true. Let's first set up our two hypotheses:

H_0: u = 100
H_1: u > 100

The first step is to find the rejection region. Given that a = 0.05, we want the probability of falling into the rejection region to be 0.05, assuming the null hypothesis is true. For a one-tailed normal distribution, a = 0.05 corresponds to a z value of 1.645. Thus, we want to solve for X ...

Solution Summary

The probability of randomly selecting a red haired person form this distribution is given. The probability that one of them will wear blue to class is given.

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